To tackle with the support-query shift, optimal transportation [1]} is one of the effective techniques to align different distributions by a transportation plan \(\pi (\mu _s, \mu _q)\) , which can formally be written as follows.
\(\small W (\mu _s,\mu _q)= \inf _{\pi \in \Pi (\mu _s,\mu _q)} \int w(x_s,x_q)d\pi (x_s,x_q),\) 
